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One of the bestloved Englishlanguage books for children is The Wonderful Wizard of Oz by L. Frank Baum. It tells the story of a girl, swept by cyclone out of her native Kansas, who has adventures with a Scarecrow, a Tin Man, a Cowardly Lion and witches good and bad, searching for and finding the Wizard himself. It might also be a parable about monetary policies in late nineteenth century America; Baum himself was a politically aroused newspaper editor who had sympathy for those who wanted to get rid of the gold standard and allow the money supply to expand and interest rates to fall. The “Oz”, according to this hypothesis, could be the ounce of gold, its standard measure of quantity, the yellow brick road a path to the hidden lair of gold, and the Wizard, who, once he is no longer behind curtains appears weak and fallible, the false authority of the gold standard itself. Or not.
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Just 1 year after Keynes published his
General Theory of Employment, Interest and Money, another British economist, John Hicks published an article in which he presented a simple algebraic version of what he took to be the main argument. Most observers, including Hicks himself (later), felt that the simplification was not quite the full Keynesian treatment, but it has proved useful for generations of students and policy practitioners. The geometric version is referred to as the ISLM model, since it is based on two curves that bear these pairs of letters.
ISLM looks at Keynesian economics through the prism of financial markets. Specifically, it imagines a world in which there are two financial assets, money and bonds, each with its own market. Both markets have a supply and a demand side and are assumed to be in equilibrium. Between them, they determine the level of national income and the rate of interest that prevails at a point in time.
Let’s take the bond market first. The demand for loans, in the simplest case, comes from firms. To make things easy, let’s say that this borrowing exactly finances their investment: there is no source of funds for investment other than loans, and all loans are used to make investments. To make any further progress we need a model of what determines the firms’ desired level of investment.
So consider a simple linear (straightline) investment function such as
where a is the level of desired investment if the interest rate is zero, b is a slope, and i is the interest rate. Visually it looks like this Fig.
13.5 on the following page.
As the interest rate falls, investment increases, topping out at
a when the interest rate reaches zero on the horizontal axis. At some higher rate of interest such as i
_{0} the formula in Eq.
13.1 tells us to subtract −b times i
_{0} from a to get the resulting level of desired investment. Realworld investment functions would be more complicated than this, of course, but we would still expect that, all other things being equal, a higher cost of borrowing (i) would result in less desired investment.
The investment function in Fig.
13.5
provides the demand curve in the market for loans.
where Y is income, C is consumption, T is tax payments, C
_{0} is autonomous consumption, MPC is the marginal propensity to consume and t is the tax rate.
Solving for S, we get
This looks more complicated than it is. All it says is that savings is the portion of income not spent on consumption, MPC (1−t), or taxes, t, or autonomously, C
_{0}. Look at the parenthetical expression after Y in identity Eq.
13.3: it’s a positive fraction, something between 0 and 1. This means that, as Y goes up, so does S. And that makes sense, since the more income people have, the more they are intending to save, at least according to the simple consumption function we introduced in Chap.
11.
What this means is that the supply of savings made available to firms is simply a function of income. So put supply and demand together: the lower the rate of interest, the more firms want to borrow. The higher the level of national income, the more households want to save. We know that in this simple model savings are always identically equal to investment. So do a thought experiment: suppose the market for loans is in equilibrium, but then the interest rate goes down. This means firms will want to borrow more. That is only possible if households supply more savings, so, since the investmentsavings identity
must hold, it must also follow that national income must be higher. To put it differently, there is one potential equilibrium with a higher interest rate and a lower national income, and another at a lower interest rate and a higher national income. What you can’t have is a shift in one without the other, since that would violate the investmentsavings identity. Of course, this is not some bit of economic magic: if firms borrow and invest more, they simultaneously (through their spending on investment) generate additional income out of which households can save. The reason it all works out is that we have a simple model where there is no alternative: the algebra mandates that it
has to work out.
This reasoning is the basis for the
IS curve, as depicted in Fig.
13.6.
where M
^{D} is the demand for money, c is the transaction demand effect of income Y, L is desire for extra liquidity, and −d i is the effect that the opportunity cost of interest income has on the liquidity demand. The sum of transaction demand (c Y) and liquidity demand (L − d i) is the total demand to hold money.
Now add one more assumption, that the money supply is under the control of the central bank, which sets it at the level it chooses for monetary policy purposes. This can be written as
In other words, the money supply, according to this assumption, is fixed at some exogenous level. Equilibrium in the money market requires that M
^{S} = M
^{D}; therefore
In order for this to be, there is an implicit relationship between Y and i. If Y goes up there will be more transaction demand, which means there must be
less liquidity demand (to keep overall demand equal), and this in turn implies that the interest rate must be higher: higher interest rates discourage people from holding money to simply assuage their apprehensiveness. Similarly, if interest rates fall, liquidity demand for money rises, so transaction demand must fall, meaning that spending and income must be lower. Putting it altogether, this threeway relationship between national income, interest rates and money demand (which must equal money supply) can be depicted geometrically as in Fig.
13.7 on the next page.
If national income is at some particular level Y
_{0}, the
LM curve tells us what the interest rate needs to be so that total money demanded equals money supplied.
Note that the LM curve depends on the assumption that the central bank is willing and able to control the money supply. As we saw in Chap.
7, however, this is no longer the case (if it ever really was) in modern financial systems. That might be seen as a big problem for the ISLM story we are telling. Another approach has been proposed, however, in which the central bank sets interest rates (not the money supply) on automatic pilot: whenever national income goes up, this robopolicy machine reflexively raises interest rates and vice versa. That would give us an LM curve like the one in Fig.
13.7 too. For the purposes of this
Appendix, however, we will stick with the centralbankcontrolsthemoneysupply version of the story, since it is still the common approach used in economics textbooks. (The robopolicy justification for LM illustrates how some economists are beguiled by the notion of a central bank that follows predetermined rules and refuses any form of discretionary policy. This will play an important role in Chaps.
15 and
16.)
The IS curve represents equilibrium combinations of national income and the interest rate in the bond market. The demand for loans increases as interest rates fall, and the supply of savings increases as income rises. Thus the equilibrium condition that supply equals demand can arise either at higher interest rates and lower income or lower interest rates and higher income. These possibilities are incorporated in the IS curve, which is downwardsloping.
The LM curve represents equilibrium combinations of national income and the interest rate in the money market. In this case the supply of money is assumed to be determined independently by the central bank. The demand for money has two components, transaction demand (positively related to national income) and liquidity demand (negatively related to the interest rate). Since these must sum to a fixed money supply, higher income is associated with a higher interest rate; the LM curve is upwardsloping.
External shocks or policy changes can be represented by a shift in the appropriate curve. Shocks that alter the desire to invest or save out of income affect the IS curve; shocks that alter the desire to hold stocks of money alter the LM curve. Fiscal policy shifts the IS curve, monetary policy the LM curve.
Under extreme circumstances, the IS and LM curve may not intersect at a positive interest rate; this is referred to as a liquidity trap. When that arises, ordinary monetary policy is ineffective, and fiscal policy is required to have an impact on national income.
ISLM incorporates three Keynesian ideas in a single model: the central importance of desired spending on the part of firms and households, the role of liquidity preference in response to the unpredictability of the economic environment, and the notion that the level of national income is not predetermined but fluctuates in order to achieve equilibrium in the key markets of a capitalist economy. It is not a perfect representation of the position Keynes put forward in
The General Theory, however, and it has played a smaller role in theory and policy as the influence of Keynesianism itself diminished in recent decades.
IS curve
Liquidity demand for money
Liquidity trap
LM curve
Transaction demand for money
Zero lower bound
$$ {\mathrm{I}}^{*}=\mathrm{a}\mathrm{b}\ \mathrm{i} $$
(13.1)
×
What about supply? That comes from households in our verysimple model. Household savings are what is left over after spending. (Note that we are assuming that all investment is domestically financed, which means either that there is no foreign trade or investment, or that the current and capital accounts remain in balance at all times. There is a more sophisticated version of ISLM that drops this assumption, but we won’t develop it here.) Using similar algebra to Chap.
11, we begin with the identity that all income is either spent, saved or paid in taxes.
$$ \mathrm{Y}\equiv \mathrm{C}+\mathrm{T}+\mathrm{S}\equiv {\mathrm{C}}_0+\mathrm{MPC}\left(1\mathrm{t}\right)\mathrm{Y}+\mathrm{t}\ \mathrm{Y}+\mathrm{S}\equiv {\mathrm{C}}_0+\mathrm{Y}\left(\mathrm{MPC}\left(1\mathrm{t}\right)+\mathrm{t}\right)+\mathrm{S} $$
(13.2)
$$ \mathrm{S}\equiv \mathrm{Y}\left.\left(1\mathrm{MPC}\left(1\mathrm{t}\right)\mathrm{t}\right)\right){\mathrm{C}}_0 $$
(13.3)
×
At some rate of interest i
_{0} the curve locates for us the corresponding level of equilibrium national income, Y
_{0}. This is the level of income at which households generate just the level of savings to lend to firms so they can make the investments they choose at interest rate i
_{0}. As interest rates fall, desired investment and borrowing rises and so must national income. The opposite happens if interest rates rise.
Now what about the LM half of the story? This one is somewhat more complicated and takes us into the demand for money. In general there are two reasons why people would want to hold money, to spend it or to keep it in reserve as a buffer against unforeseen events. The first is called the
transaction demand for money, and it is assumed to be a simple function of the overall level of spending, and therefore income, in the economy. The second is the
liquidity demand; it is a function of two things, how apprehensive people feel about the future (and therefore their desire to hold extra money as a safeguard) and the prevailing rate of interest, which is the opportunity cost of holding money. This second point is essential. To simplify the situation, if people have extra savings they don’t intend to spend, they can hold it in the form of money or they can use it to buy other financial assets. These financial assets pay a rate of interest, so if they choose money instead they lose the benefit of this potential return. The higher the interest rate on such assets, like government bonds, the greater the cost of holding money.
Algebraically, the demand for money can be expressed, again in linear fashion, as
$$ {\mathrm{M}}^{\mathrm{D}}=\mathrm{c}\ \mathrm{Y}+\left(\mathrm{L}\mathrm{d}\ \mathrm{i}\right) $$
(13.4)
$$ {\mathrm{M}}^{\mathrm{S}}={\mathrm{M}}_0^{\mathrm{S}} $$
(13.5)
$$ {\mathrm{M}}^{\mathrm{S}}=\mathrm{c}\ \mathrm{Y}+\left(\mathrm{L}\mathrm{d}\ \mathrm{i}\right) $$
(13.6)
×
Now that we have the two iconic pieces individually, it is just a small step to put them together in a single diagram (Fig.
13.8).
×
The bond market is in equilibrium at any point along the IS curve, and the money market is in equilibrium at any point along the LM curve. Both are in equilibrium simultaneously where they intersect, which in this diagram is at national income Y
^{*} and interest rate i
^{*}. In other words, by incorporating (very) simple models of these two financial markets, the ISLM model provides insight into how the size of the economy and the interest rate are determined.
Bear in mind, however, that these curves are not “things”. There are no IS or LM curves visible in the actual economies we live in, nor can they really be measured with the data we have available to us. They are purely aids to thought—intellectual constructs that make it a bit easier to think systematically about the interaction between different factors that affect the economy.
For instance, we all know that there is a tendency for lower interest rates to lead to more rapid economic growth; that’s the entire point of monetary policy, after all. This tendency is captured in a rough form in the IS curve. At the same time, we know from experience that as an economy heats up—as its growth rate expands—there is also a tendency for interest rates to rise. (Sometimes interest rates rise even before growth sets in from the expectation of financial market players that economic growth is on the way.) This countertendency is reflected in the LM curve.
Both tendencies are at work simultaneously. It is not all one or the other, and the ISLM model gives us a way to understand how this is possible.
The main use of the model lies in thinking through the consequences of different events that may alter the course of the economy, either external shocks or policy changes that are deliberately intended to promote or dampen growth. Representing these events in an ISLM diagram is a lot like representing changes in market conditions in a supply and demand diagram. In both cases, the key is knowing which curve shifts and in which direction, while the other stays in place.
Let’s start with an example. Suppose business expectations become more pessimistic. It might happen, for instance, that those in charge of business investment revise downward their forecast of consumer demand over the coming year. This will reduce their desire to invest at any interest rate. This will reduce the
demand for loans, which is a component of the IS curve. That being the case, it will take a smaller
supply of savings to achieve equilibrium in the bond market. That in turn signifies that national income will be lower for this equilibrium to occur. Graphically, the result is as pictured in Fig.
13.9 on the following page.
×
This falloff in the demand for loans, which was presented as an external shock, moves the IS curve to the left. At any interest rate it will take less national income to generate the savings needed to reach equilibrium in the loan market. The result is that equilibrium national income falls from Y
^{*}
_{1} to Y
^{*}
_{2}, while interests will also fall from i
^{*}
_{1} to i
^{*}
_{2}. Note that this is represented by movement
along the LM curve: the money market will now be in equilibrium at a lower level of national income (less transaction demand for money) and a lower interest rate (more liquidity demand) as well.
Now let’s try a policy move by the central bank. Suppose it is decided to increase the money supply in order to spur economic growth. This obviously works directly on the money market, which gives us the LM curve. And which way does the curve shift? A new equilibrium in the money market will also entail more money demand, which must involve some combination of more transaction demand (higher income) and more liquidity demand (lower interest rate). In other words, the LM curve shifts to the
right and
down, as in Fig.
13.10.
×
The new intersection of IS and LM occurs at a higher level of national income, Y
^{*}
_{2}, and also the lower interest rate i
^{*}
_{2}. This is what we would expect: expansionary monetary policy has lowered interest rates and raised growth (to a higher level of income). The IS curve, meanwhile, sits still because nothing has happened to cause it to shift; the movement resulting from the monetary policy change is
along the IS curve.
The ISLM model, despite its limitations, helps us to think coherently about monetary and fiscal policy. For instance, suppose that, instead of expansionary monetary policy, public officials decided on fiscal expansion instead—more government spending and/or lower taxes. How would this have differed in its effects? ISLM can give you the answer. Consider which curve would shift in which direction and how this would affect the location where IS and LM intersect each other. (Hint: it’s partly the same in its effects as expansionary monetary policy and partly different.)
There is one final wrinkle of considerable importance that needs to be considered. Just because we can draw two curves, one upwardsloping and the other downwardsloping, in a quadrant doesn’t mean they have to cross! In the micro text there was an example of a product for which the supply curve was always above the demand curve; such a product would never be produced in a normal market economy. We will do a similar thing with ISLM.
Suppose we have a situation in which either the LM curve is so far to the right or the IS curve so far to the left that they don’t cross at a positive rate of interest, as in Fig.
13.11.
×
Why would this happen? Above all, it may be the case that there is simply very little loan demand in the economy; businesses are
extremely pessimistic about future prospects and have little desire to invest, no matter how low the interest rate falls. In a more realistic version of the model where households as well as firms may be borrowers, it may equally be households that abjure taking on debt. And recall that borrowing is reduced whenever someone pays off a loan. This is an important insight: there are times when either businesses or household or both are eager to pay down debt that they had previously acquired. This shows up as a deduction from the demand for loans, pushing the IS curve to the left.
So why can’t the LM curve descend into negative interest rate territory in order to intersect a negativeinterestrate IS? Quite simply, who would lend at a negative interest rate? You would be better off just hanging on to your money; a negative interest rate would mean that the lender pays the borrower for the privilege of borrowing—not a chance. So the interest rate cannot fall below zero. This is referred to as the
zero lower bound. Monetary policy can bring the rate down to this point and no further. If the LM curve is to the right of the IS, pumping money into the economy will do little good. In a phrase made famous during the Great Depression, expanding the money supply under such circumstances is like “pushing on a string”. Only fiscal policy, shifting the IS curve, can do the job.
There is one possible monetary policy escape hatch from the liquidity trap, however. In our survey of ISLM we haven’t mentioned inflation; it isn’t clear whether Y and i are measured in real or nominal terms. That was deliberate: it’s another complication, and the goal was to present the model in its simplest possible form. Nevertheless, it is important to note that, while
nominal interest rates can’t be negative,
real interest rates can be. This would arise if the nominal rate is at or near zero (the zero lower bound) while inflationary expectations are strongly positive. A nominal interest rate of zero combined, for instance, with expected inflation of 4 % per year translates into a real interest rate of −4 %. In effect, this would push us into negative interest rate territory and allow further movement down the IS curve—the path of expansionary monetary policy. As this is being written, such measures are being undertaken in Japan and a broad crosssection of economists are calling for similar efforts in Europe and the US.
To sum up, what’s Keynesian about ISLM? Three things:
First, the willingness of households and firms to spend on currently produced goods and services is fundamental. In the simple model we presented here, the only factor that influences them is the interest rate. This shows up in the assumption that business investment I varies inversely with interest rate i, a building block of the IS curve. If we added household borrowing to the mix, we could extend this insight to the rest of the economy. (The housing market, financed through mortgage lending, is a key element in the business cycle, for instance.) Consumer spending appears indirectly in the IS curve through the influence that the marginal propensity consume plays in determining the level of savings. As we’ve developed it here, it is simply a black box; no theory was offered to explain why it would go up or down over time. Nevertheless it’s there, and it produces Keynes’ paradox of thrift: the lower the MPC, and therefore the higher the fraction of income consumers wish to save, the lower the level of national income produced by the equilibration process encompassed in the IS curve. In simple terms, if households are subject to a wave of thriftiness, the IS curve shifts to the left.
Second, the role of liquidity preference, the desire of participants in the economy to hold money against an uncertain future, is incorporated in the LM curve. The greater the liquidity demand for money, the lower the transaction demand for any given level of the money supply, and this means a lower equilibrium level of national income. In previous economic theories, money was simply a medium of exchange, but for Keynes it was also an asset, valued for its ability to limit risk and enable the exploitation of unexpected opportunities. He knew it was not simply a matter of hoarding; it didn’t make sense to say that money was being siphoned off into mattresses, safes and vaults, since in a modern economy nearly all money does circulate one way or another. Rather, the desire to hold a larger share of wealth in the form of money would affect the economy by putting upward pressure on interest rates. This is what happens when the LM curve shifts the left, meaning that more liquidity demand has entailed less transaction demand for any given money supply, and the economy moves up the IS curve.
Finally, and most critically, the ISLM apparatus incorporates the insight that the level of national income in an economy adjusts, along with other variables, to bring about a state of equilibrium. The IS curve reflects the notion that economic growth (a change in national income) is demanddriven: more desire by businesses to invest, more desire by households to spend out of their income, and expansionary fiscal policy by government all push this curve to the right and bring about a higher rate of economic growth. The LM curve conveys the message that money is not neutral, as it would be if the only function it performed was to serve as a medium of exchange. Instead, expansion of the money supply or measures to induce wealthholders to reduce their desire to hold it in the form of money will push the LM curve to the right, and the economy will expand.
The advantage of ISLM is that it reflects all of these ideas simultaneously in a single, interconnected model. Our Keynesian Cross (Chap.
11) didn’t do that; all it did was to connect desired spending to equilibrium income. It didn’t have any financial markets, and it didn’t tell us anything about interest rates. For this reason it was unable to incorporate monetary policy, much less show how fiscal and monetary policy interact. In this sense, ISLM is “closer to Keynes”. On the other hand, there are important aspects of Keynesian thinking that are missing or perhaps even misrepresented by ISLM. As was mentioned earlier, the model leaves out international trade and finance. There are more sophisticated versions that try to do this, but none of them is entirely satisfactory. (That’s a topic for a more advanced course in open economy macroeconomics.) Another shortcoming is that the LM curve relies on ad hoc assumptions that are not in the spirit of Keynes’ work, and are factually incorrect to boot. The central bank does not control the money supply. Keynes was deeply involved in monetary policy, and he understood and wrote extensively on the interactions between money creation and the “real” economy. The money supply for Keynes was the combined outcome of central bank policy, economic institutions, and trends in consumption and investment—not a given but something to be determined. And Keynes never imagined that a rigid, rulebased monetary policy should be brought into a general theory of how market economies work, as in the alternative version of the LM curve; for him the purpose of an economic model was to inform policymakers so they could make both the rules and the exceptions that the economy needed at any moment in time.
Of course, a different criticism of ISLM might be that what we need is the best possible model of how the economy works, and that we won’t find it in Keynes, period. That was the view that become dominant over the course of the 1970s, as we will see in Chap.
15. By the final years of the twentieth century, ISLM had begun to disappear from textbooks and was regarded as hopelessly primitive by the trendsetters in macroeconomic theory and policy. It has made a partial comeback in the wake of the 2008 financial crisis, since, equation for equation, it seems to do a better job of explaining economic conditions and predicting the effects of monetary and fiscal policies than the main alternatives.
1.
The IS curve represents equilibrium combinations of national income and the interest rate in the bond market. The demand for loans increases as interest rates fall, and the supply of savings increases as income rises. Thus the equilibrium condition that supply equals demand can arise either at higher interest rates and lower income or lower interest rates and higher income. These possibilities are incorporated in the IS curve, which is downwardsloping.
2.
The LM curve represents equilibrium combinations of national income and the interest rate in the money market. In this case the supply of money is assumed to be determined independently by the central bank. The demand for money has two components, transaction demand (positively related to national income) and liquidity demand (negatively related to the interest rate). Since these must sum to a fixed money supply, higher income is associated with a higher interest rate; the LM curve is upwardsloping.
3.
External shocks or policy changes can be represented by a shift in the appropriate curve. Shocks that alter the desire to invest or save out of income affect the IS curve; shocks that alter the desire to hold stocks of money alter the LM curve. Fiscal policy shifts the IS curve, monetary policy the LM curve.
4.
Under extreme circumstances, the IS and LM curve may not intersect at a positive interest rate; this is referred to as a liquidity trap. When that arises, ordinary monetary policy is ineffective, and fiscal policy is required to have an impact on national income.
5.
ISLM incorporates three Keynesian ideas in a single model: the central importance of desired spending on the part of firms and households, the role of liquidity preference in response to the unpredictability of the economic environment, and the notion that the level of national income is not predetermined but fluctuates in order to achieve equilibrium in the key markets of a capitalist economy. It is not a perfect representation of the position Keynes put forward in
The General Theory, however, and it has played a smaller role in theory and policy as the influence of Keynesianism itself diminished in recent decades.

IS curve

Liquidity demand for money

Liquidity trap

LM curve

Transaction demand for money

Zero lower bound
 Titel
 Central Banks and Monetary Policy
 DOI
 https://doi.org/10.1007/9783642374418_13
 Autor:

Peter Dorman
 Verlag
 Springer Berlin Heidelberg
 Sequenznummer
 13
 Kapitelnummer
 13